The bill, named after Republican Sens. Lindsey Graham (S.C.) and Bill Cassidy (La.), aims to give more control over health care to states. It would convert ObamaCare's insurer subsidies and Medicaid expansion funds into block grants, so that states can design their own programs.

The poll was highlighted by several Democratic groups seeking to defend the Affordable Care Act.

In addition, 46 percent of voters said they would be less likely to vote for a member of Congress if he or she voted for Graham-Cassidy, while 23 percent would be more likely.

Seventy-seven percent said they agreed with late-night host Jimmy Kimmel that no one should be denied coverage because they cannot afford it.

The Senate is set to possibly vote next week even without a Congressional Budget Office analysis of the measure's effect on premiums and the number of people covered. In the poll, 68 percent of voters said lawmakers should wait to get that analysis, and 21 percent said they should vote anyway.

This bill does appear to be polling at least somewhat higher than the earlier GOP ObamaCare repeal bill, which got just 12 percent approval in a USA Today/Suffolk University poll in June.